Nonnegative matrix factorization
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then <math>Y\!=U^\star U^{\star\rm T}.</math> | then <math>Y\!=U^\star U^{\star\rm T}.</math> | ||
+ | <br> | ||
In summary, initialize <math>Y=I\,</math> then alternate solution of | In summary, initialize <math>Y=I\,</math> then alternate solution of | ||
Revision as of 14:27, 28 September 2009
Example from Convex Optimization & Euclidean Distance Geometry, ch.4:
Given rank-2 nonnegative matrix
find a nonnegative factorization
by solving
which follows from the fact, at optimality,
Use the known closed-form solution for a direction vector to regulate rank (rank constraint is replaced) by Convex Iteration;
set to an ordered diagonalization and
,
then
In summary, initialize then alternate solution of
with